What specific action fulfills the commandment to write a sefer torah?
At my synagogue we're currently writing a sefer torah in honor of our retiring rabbi. I know that the 613th mitzvah is to write a sefer torah, and have been taught that participating in the writing of one fulfills the obligation -- we don't each have to write our own complete scroll.
I understand that the conventional way to do this is to make a financial donation and then sit with the sofer (scribe) and touch the sofer's hand (or arm) while a letter is written. In the activities at my synagogue I've seen the result referred to as "your letter". (For example, the honoree got the beit in B'reisheet as "his" letter.) Or sometimes it's words, verses, chapters, or parshiyot, depending on the size of the donation.
What part of this actually effects "writing a sefer torah"? If someone makes a donation but doesn't sit with the sofer, has that person fulfilled the obligation? If the person declares the intent to participate but doesn't make a donation, is that enough? (For example, maybe writing a sefer torah is a community activity and all members of the community have a share without funding it.)
If one fulfills the obligation only by physically assisting with the writing, I have a followup question: what happens if the sofer makes a mistake? I saw a case with a spelling error, which will require the sofer to scrape off and rewrite text that people participated in.